A brief essay about the Melody Theatre on this web page says that the house opened in March, 1946, and was closed and the building converted into a church in 1952.

The primary cause of the Melody’s short life appears to have been the rivalry of the East Side Theatre, which a 1948 lawsuit alleged had an unfair advantage due to its relationship with distributors, as told in this article from Motion Picture Herald of September 18, 1948:

“Files Trust Suit In Savannah

“Charging there was a conspiracy to force him out of business and to monopolize product for rival Negro theatres, Mose Portman, Melody Theatre Co., and East Broad Investment Co., last week filed a $957,264 anti-trust action in Federal Court at Savannah, Ga. Defendants include: Bijou Amusement Co., Savannah East Side Corp., Dunbar Theatre Corp., Fred G. Weis, president of Savannah East Side; G. T. Bailey, Harold T. Spears, Alfred Starr and Milton Starr of Bijou, and seven major motion picture distributors.

“The distributors named are Paramount, Warners, Columbia, Republic, RKO, Loew’s and United Artists.

“The complaint charges that Savannah East Side built a theatre for Negroes in opposition to Mr. Portman’s Melody, built in 1946, and that Melody Theatre Company was forced to sell the house because the distributors conspired to divert first class product to the opposition theatre interests, thus depriving the Melody of product.”

I haven’t found anything about the outcome of the suit, but given that the Melody closed by 1952 I’m guessing it didn’t help.